9626375 Grove The project deals with global problems in Riemannian geometry. The investigator intends to study approximations of Riemannian manifolds by singular spaces such as Alexandrov spaces and finite metric spaces; to study stability and inverse stability problems for Riemannian manifolds; to investigate the relationship between curvature and symmetry of Riemannian manifolds via the geometry of orbits; to find examples of manifolds with large isometry groups and with positive curvature. Riemannian manifolds are an abstraction of curved spaces possessing a distance function. Unlike curves and surfaces in 3-space these manifolds do not necessarily sit inside an ambient space, hence they are abstract spaces. The proposed research aims to understand various global aspects of these manifolds, in particular, the investigator is interested in approximations of Riemannian manifolds by finite metric spaces and in symmetry properties. Finite metric spaces are closely related to graphs so that the project may impact on discrete applications of Riemannian geometry.

Agency
National Science Foundation (NSF)
Institute
Division of Mathematical Sciences (DMS)
Type
Standard Grant (Standard)
Application #
9626375
Program Officer
Christopher W. Stark
Project Start
Project End
Budget Start
1996-06-01
Budget End
1999-09-30
Support Year
Fiscal Year
1996
Total Cost
$135,000
Indirect Cost
Name
University of Maryland College Park
Department
Type
DUNS #
City
College Park
State
MD
Country
United States
Zip Code
20742